Upon electrostatic interactions, the mixture of oppositely charged macromolecules separates into a macromolecule-rich phase coexisting with a diluted phase. The phase separation is either a liquid-liquid phase separation (LLPS) forming complex coacervates, or a liquid-solid phase separation (LSPS) forming aggregates. Here, we investigate the assembly of the positively charged protein lysozyme (LYS) with the negatively charged polysaccharide alginate (ALG) at pH 7 under different conditions of mixing ratios, total concentration, and ionic strength using a droplets-based millifluidic device. A 3D phase diagram, with the concentrations of salt, lysozyme, and alginate as the 3D coordinates, gives a thorough description of the monophasic, liquid-solid, and liquid-liquid phase separation areas and the regions where both solid and liquid phases coexist. The thermodynamic aspects behind these two kinds of complex formation are investigated using isothermal titration calorimetry (ITC). Aggregation is associated with a strong affinity between LYS and ALG, with a 100 LYS : 1 ALG stoichiometry ratio, whereas coacervation at higher salt concentration is asso- ciated to a strong decrease of the binding affinity between the two biopolymers.